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Using the Euclidean metric, is the set (0, 1) in R^2 open, closed, both, or neither?

  1. Feb 19, 2012 #1
    I typed the question and my attempt at a solution below...

    euclidmetric.png

    It seems obviously open to me, but I'm not sure how to state it using open balls considering that it's in R^2.
     
  2. jcsd
  3. Feb 19, 2012 #2
    Re: Using the Euclidean metric, is the set (0, 1) in R^2 open, closed, both, or neith

    If it's open, its complement is closed. What happens if you sneak up to it from above? Or below?
     
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